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Suppose I charge a sphere and leave it in vacuum for 10 years. After that time, I want its surface charge density to be in the order of 10^5C/m^2. Would that be possible? Would it depend on the material used and how? Would adding or removing electrons make a difference (positively vs negatively charged)?

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Why would there be a limit in vacuum? –  Mr.ØØ7 Apr 27 '13 at 5:03
    
Thank you for your answer. I kind of see your point, if it is a hypothetical, perfect sphere. I don't suppose that even in that case we could add an infinite number of electrons, but maybe I am wrong. My question though, is about a sphere that we could actually build. Wouldn't it necessarily have imperfections that would allow electrons to escape? –  Christopher Akritidis Apr 27 '13 at 7:45

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If you take, for example, a perfect metal sphere then it has a work function that is the energy required to remove an electron from the metal to infinity. If you start charging the sphere by adding electrons to it then the work function decreases, and above some limiting charge the work function falls to zero. This means any more electrons you add to the sphere immediately escape again. This is an example of a phenomenon is called field emission.

I've chosen the example of a metal sphere since it's nice and simple, but this will apply to any object, and it means that there is a maximum charge that can be sustained on any object regardless of how close to perfectly it has been made.

If you keep the charge below the level where field emission occurs, and keep the object in a vacuum, and mask it from any light with energy of greater than the work function, and keep it at a temperature below which thermionic emission occurs, then the sphere will stay charged forever.

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Thank you John, your answer definitely sets me on the correct path. –  Christopher Akritidis Apr 27 '13 at 14:52
    
Based on John’s answer, I found the following calculator: pulsedpower.net/Applets/pulsedpower/fieldemission/… I can’t vouch for its accuracy, but I entered the following: Electric Field of Conducting Sphere E = Q/(4*π*r^2*ε0) = D/ε0 ε0 = ~10^-11 F/m is the vacuum permittivity => E = ~10^5/10^-11 V/m = ~10^16V/m (= 10^8MV/cm) Surface is 4πR^2 = 10*100μm^2 =1000μm^2 The electron wave function of metals is in the order of eV The result was that the field emission effect was way too high for ordinary electron wave functions. –  Christopher Akritidis Apr 27 '13 at 16:23

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